The Ghana international will continue his career in Serie A after he was deemed surplus to requirements at Chelsea
The Ghana international was no longer needed at the Premier League giants and will now be looking to relaunch his career at the San Siro outfit.
Essien has signed a 18-month deal with Milan and will be unveiled to the press on Tuesday afternoon at 13:00CET.
"To show Michael respect is to not stop him going," Chelsea manager Jose Mourinho commented on the 31-year-old's departure.
"We would have been happy had he stayed because he is fantastic player for the team, but he's given everything for the club and a great chance arrived for his future.
"I know he can continue to play at a high level and I wish him success and happiness in Italy and at the World Cup in Brazil."
Essien started his professional career with Bastia and also wore the Olympique Lyonnais jersey before joining Chelsea in 2005.
He won two Premier League titles, four FA Cups and the Champions League during his time with the Blues. The midfielder was shipped out on loan to Real Madrid last season.
The midfielder is Milan's third signing of the January transfer window after the previous arrival of Keisuke Honda and Adil Rami from CSKA Moscow and Valencia, respectively.